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Imagine that in the course of your analysis, you regularly require summaries of numerical values. For some applications you want the mean of that quantity, plus/minus a standard deviation; for other applications you want the median, and perhaps an interval around the median based on the interquartile range (IQR). In either case, you may want the summary broken down with respect to groupings in the data. In other words, you want a table of values, something like this:

For a specific data frame, with known column names, such a table is easy to construct using dplyr::group_by and dplyr::summarize. But what if you want a function to calculate this table on an arbitrary data frame, with arbitrary quantity and grouping columns? To write such a function in dplyr can get quite hairy, quite quickly. Try it yourself, and see.

I am working on some practical articles on variable selection, especially in the context of step-wise linear regression and logistic regression. One thing I noticed while preparing some examples is that summaries such as model quality (especially out of sample quality) and variable significances are not quite as simple as one would hope (they in fact lack a lot of the monotone structure or submodular structure that would make things easy).

That being said we have a lot of powerful and effective heuristics to discuss in upcoming articles. I am going to leave such positive results for my later articles and here concentrate on an instructive technical negative result: picking a good subset of variables is theoretically quite hard. Continue reading Variable pruning is NP hard

Monads are a formal theory of composition where programmers get to invoke some very abstract mathematics (category theory) to argue the minutia of annotating, scheduling, sequencing operations, and side effects. On the positive side the monad axioms are a guarantee that related ways of writing code are in fact substitutable and equivalent; so you want your supplied libraries to obey such axioms to make your life easy. On the negative side, the theory is complicated.

Let’s take a break from statistics and data science to think a bit about programming language theory, and how the theory relates to the programming language used in the R analysis platform (the language is technically called “S”, but we are going to just call the whole analysis system “R”).

Our reasoning is: if you want to work as a modern data scientist you have to program (this is not optional for reasons of documentation, sharing and scientific repeatability). If you do program you are going to have to eventually think a bit about programming theory (hopefully not too early in your studies, but it will happen). Let’s use R’s powerful programming language (and implementation) to dive into some deep issues in programming language theory:

References versus values

Function abstraction

Equational reasoning

Recursion

Substitution and evaluation

Fixed point theory

To do this we will translate some common ideas from a theory called “the lambda calculus” into R (where we can actually execute them). This translation largely involves changing the word “lambda” to “function” and introducing some parenthesis (which I think greatly improve readability, part of the mystery of the lambda calculus is how unreadable its preferred notation actually is).

We’ve just finished off a series of articles on some recent research results applying differential privacy to improve machine learning. Some of these results are pretty technical, so we thought it was worth working through concrete examples. And some of the original results are locked behind academic journal paywalls, so we’ve tried to touch on the highlights of the papers, and to play around with variations of our own.

One of the things I like about R is: because it is not used for systems programming you can expect to install your own current version of R without interference from some system version of R that is deliberately being held back at some older version (for reasons of script compatibility). R is conveniently distributed as a single package (with automated install of additional libraries).

Want to do some data analysis? Install R, load your data, and go. You don’t expect to spend hours on system administration just to get back to your task.

Python, being a popular general purpose language does not have this advantage, but thanks to Anaconda from Continuum Analytics you can skip (or at least delegate) a lot of the system environment imposed pain. With Anaconda trying out Python packages (Jupyter, scikit-learn, pandas, numpy, sympy, cvxopt, bokeh, and more) becomes safe and pleasant. Continue reading Thumbs up for Anaconda

Modern text encoding is a convoluted mess where costs can easily exceed benefits. I admit we are in a world that has moved beyond ASCII (which at best served only English, and even then without full punctuation). But modern text encoding standards (utf-x, Unicode) have metastasized to the point you spend more time working around them than benefiting from them.

Here is a neat example of famous mathematician Pál Erdős (often rendered in English as Paul Erdős) writing like a programmer in 1961. He goes to some trouble to introduce notation that allows him to index everything from zero. Continue reading Erdős writing like a programmer

For more and more clients we have been using a nice coding pattern taught to us by Garrett Grolemund in his book Hands-On Programming with R: make a function that returns a list of functions. This turns out to be a classic functional programming techique: use closures to implement objects (terminology we will explain).

It is a pattern we strongly recommend, but with one caveat: it can leak references similar to the manner described in here. Once you work out how to stomp out the reference leaks the “function that returns a list of functions” pattern is really strong.

As John mentioned in his last post, we have been quite interested in the recent study by Fernandez-Delgado, et.al., “Do we Need Hundreds of Classifiers to Solve Real World Classification Problems?” (the “DWN study” for short), which evaluated 179 popular implementations of common classification algorithms over 120 or so data sets, mostly from the UCI Machine Learning Repository. For fun, we decided to do a follow-up study, using their data and several classifier implementations from scikit-learn, the Python machine learning library. We were interested not just in classifier accuracy, but also in seeing if there is a “geometry” of classifiers: which classifiers produce predictions patterns that look similar to each other, and which classifiers produce predictions that are quite different? To examine these questions, we put together a Shiny app to interactively explore how the relative behavior of classifiers changes for different types of data sets.